I think every show that goes beyond 4-5 seasons drops. Some shows drop after a season or two, even. But where Community or Friends, while obviously worse than their earlier episodes, were still good shows throughout their run, HIMYM went from being good to being atrocious. Friends' season 9/10, easily their worst periods, were as good, if not better, than pretty much every other sitcom season that has followed them. I'd say that HIMYM first 3-4 seasons have a case of being better (but not by much, certainly not at the level of Friends' season 2/3) but afterwards they dipped to a level that, had they debuted that way, would have been cancelled within 6 episodes. Or perhaps not, since lots of lowest-common-denominator shows are very successful.
The reason why The Big Bang Theory, for example, doesn't get the same grief as HIMYM, despite being a similar brand of humor and having clearly gotten worse, is that their characters have developped properly and have not been turned into caricatures for the sake of forcibly manufacturing a gag to rely on as a crutch). The jokes aren't as funny (they were never that funny to begin with), but they have not shat the bed, yet.
It's hard to blame HIMYM's writers, I guess. I mean, all the well-written shows (Community, 30 Rock, Arrested Development) get no ratings while Michael Sheen tears it up. It is commercially better for a TV show to be shit than be funny. Every once in a while I turn on the comedy channel and see all these new shitcoms and think 'hey, maybe one of these is good', and tune in for an episode. You always see the same jokes, the same set-ups, the same situations, and rarely are they at least done properly to begin with. I would watch another Ross-Rachel narrative, even if it isn't original, but it needs to be funny. I can watch a 'the odd couple'-premised show, but it needs to be funny. Shows aren't funny anymore.
I had high hopes for House of Lies but I tuned out in the 2nd season. Still have it recorded, maybe I'll give it another go so it still had its moments.